Explanation

Incidence is the epidemiological term for the number of cases of a disease meeting some case definition in a specified time period. Here we present the daily incidence – that is, the number of new cases each day – of COVID-19 for a range of countries, including Australia, of course. Each country may be using a slightly different case definition, although most of the countries presented here have been using case definitions aligned with those recommended by the WHO. Three types of case definition are used, simultaneously:

• Suspected cases
• Probable cases
• Confirmed (by laboratory test) cases

All of the data reported here are for confirmed cases, with a few exceptions (China included cases diagnosed via lung CT scan for a few days in Februrary, 20020, but we have adjusted the data for those days as far as possible to remove that anomaly.

The data are drawn from the European CDC, which has collected data from various governing agencies around the world. There are some small discrepancies between these data and those given by the Australian government, and indeed other national governemnst, due to timing issues relating to when cases are tabulated each day, and so on. However, we ebelive the the European CDC to be teh best source of automatically downloadable, machine-readable data there is right now.

Note, however, that because the confirmed case definition depends on laboratory confirmation, it is influenced by the number of lab tests (RT-PCR, reverse transcriptase polymerase chain reaction tests on nasopharyngeal swabs or sputum) done by each reporting country or jurisdiction. Obviously the number of reported cases is bounded by the number of such labs tests which are done, but the degree of under-ascertainment is also affected by the policies in place which determine which potential COVID-19 cases are tested. These policies are completely country-specific and have changed over time.

Another issue with these data is that it is vastly preferrable to analyse incidence by (presumed or definite) date of onset of symptoms, rather than by date of notification or date of reporting. Theer may be variable delays in the processing of laboratory tests and the reporting of cases to central authorities. Tabulation of incidence counts by date of onset overcomes this problem. Almost all national and jurisdictional health authorities will be collecting data on presumed date of onset for each case (although, inexplicably, it is not one of the data items on the WHO-recommended data collection form). One reason for not using date of onset is that it may be incomplete, but this ignores the fact that statistical imputation can be used to validly fill in those missing dates of onset. There are also a body of methods, collectively known as nowcasting, that use multivariate time-series models to convert data tabulated by date of notification/reporting to (estimated) date of onset. If national or jurisdictional health authorities do not have the technical capacity to undertake such value-adding to their own data, they should make the required data available to trusted partners in the academic sector who can undertake such statistical manipulation for them (or help authorities implement such processing internally).

Semi-log cumulative incidence for selected countries – the Grattan Institute chart

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This chart shows the cumulative cases of COVID-19 for selected countries on a logarithmic y-axis scale, with the dates on the x-axis converted to the number of days since each country shown exceeded 100 cumulative cases, on a linear x-axis scale (hence the name semi-log, since only one of the two axes is logarithmic).

Note that countries “peel off” the diagonal trajectory as their rate of new (incident) cases reduces. If the line for a country is horizontal, it means there are no new cases occurring there.

The curve for Australia is clearly flattening, and we are keeping good company with China, South Korea and New Zealand as the other countries with nearly horizontal trajectories. Note that after considerable initial success in containing COVID-19 spread, both Japan and Singapore are now on a upwards trajectory, but the slopes of those trajectories are much shallower than the other countries shown, indicating much slower spread in those countries.

Semi-log cumulative incidence for selected countries – aligned to start of epidemic in each country

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This chart is a variation on the previous Grattan Institute chart. It isn’t really an improvement on the Grattan chart, but is shown here to illustrate the sensitivity of the Grattan chart to the method used to align the dates on the x-axis. In the chart shown at left, the dates on the x-axis are aligned to the approximate start of the COVID-19 epidemic in each country. The start dates are chosen automatically using a non-parametric changepoint detection algorithm, (see the changepoint.np package for R). The changepoints for each country shown are as follows:

Country	Detected start of epidemic
China	2020-01-18
Singapore	2020-01-27
South Korea	2020-01-30
Japan	2020-02-12
Italy	2020-02-21
Spain	2020-02-24
Germany	2020-02-25
France	2020-02-25
USA	2020-02-26
UK	2020-02-27
Australia	2020-03-01
New Zealand	2020-03-02

Semi-log daily incidence for selected countries – aligned to start of epidemic in each country

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This is another variation on the Grattan Institute chart, but this time showing daily incidence on the y-axis, rather than daily cumulative incidence. It is basically the same information as shown in the epicurve charts in the subsequent frames (accessed via the blue rectangles at the top of the page), but all of the selected countries are shown on one plot, and the dates are aligned by the detected start of the epidemic in each country.

One problem is that the daily incidence curves are rather noisy. We can address that by smoothing them, as shown in the next frame.

Semi-log smoothed daily incidence for selected countries – aligned to start of epidemic in each country

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In this chart, we can now discern three distinct groups of countries:

• an upper group of just one, the USA, where the epidemic is still growing rapidly.
• a middle group comprising the UK and European countries
• a lower group, which includes Australia , New Zealand, South Korea, China, Japan and Singapore, which all have their local COVID-19 epidemics under control (but definitely not eradicated). Note however that Japan and Singapore are now exiting that lower group and heading upwards.

Epicurves for selected countries

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The charts shown here are epicurves – that is, daily count of incident (new) cases, using data collated by the European CDC.

Note that there are some days where the number of cases appears to spike upwards, followed by a decrease the following day. This indicates that there may be some data discrepancies in how the European CDC is capturing data from WHO Situation Reports. It underlines the importance of nations providing reliable machine-readable access to their own COVID-19 data. By “machine-readable” we mean CSV or JSON data files which are automatically downlaodable, or an API which can be queried automatically to yield such data. Neither of those are difficult to establish, yet nearly all national governments have failed to provide such data, leaving it to third-party agencies and citizen-science efforts to piece together the required data in a manner that permits ongoing analysis. There is, for example, no official machine-readable source of national COVID-19 data provided by the Australian government. As far as we are aware, NSW is the only State or Territory government that has made any effort in that direction by providing some machine-readable data, which we leverage in the \(R_{t}\) for NSW theme (see menu above).

Epicurves for selected countries (common y-axis scale)

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Forcing the y-axis scale to be the same for all the plots in this chart means that, compared to the previous chart where the y-axis could change for each country, the country with the largest number cases, in this case, the USA, appears the same, and the rest of the plots appear smaller.

This provides important context: the number of cases in the USA currently dominates relative to other countries. The bottom row of countries are barely visible, by comparison.

Epicurves for selected countries (logarithmic y-axis scale)

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The final variation the epicurve chart, show here, uses a logarithmic y-axis scale. This emphasises lower counts, which is useful for inspecting the beginnings and ends of the epicurves, or the middle parts where there is more than one “wave”, as in China and Singapore.

Explanation

To understand the spread of COVID19, we use a statistic called “R0” (R-nought). This is the number of people we expect to be infected from one COVID19 infected person arriving in a population.

We are estimating R0 from the available data, and are specifically estimating the effective reproduction number (different to basic reproduction number). This reflects the current state of a population, which may include some infections.

What does R0 mean?

If R0 is 1

• One person arriving to a population could spread it to one other person. Those people could then spread it to one other person. This is easier to manage.

If R0 is 0.3

• For every 10 people infected, it would spread to 3 other people.

If R0 is 2

• Every person arriving in the population can infect 2 more people. This can quickly get out of control.

What do we want R0 to be?

• We want the R0 to be below 1, and ideally as close to 0 as possible.

Estimating Effective reproduction number

We estimate the effective reproduction number using mathematical modelling. This means that the estimated numbers are dependent upon the mathematical model, and while they are our best possible guess at R0, they may be some inaccuracies.

These estimates reflect the number of new cases we expect from an infected person as they interact with a population. The higher the number, the worse the control of the infection, and the more people will be infected. We want this number to be below 1, and preferably as close to 0 as possible.

Misconceptions / mistakes

R0 is not a rate, and has no units of time.

This means it is not a rate of infection, and does not tell us how fast an infection spreads.

Limitations

These estimates are for all countries do not account for people who bring the infection to the population by travelling. This means that we are assuming all of these infections are spread by the community. However, Australia actually has quite a large proportion of people who are travelling from overseas with COVID19. This means that these estimates might be over-estimating R0. We have explored what is possible if we improve incorporate these imported cases, where we have this data for New South Wales.

Selected Countries

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The effective R estimates for each country indicate that most countries are bringing the spread of the virus under control. However there is some wide variation. The measurement of effective R for Australia has decreased substantially, now falling below one, indicating that we have now started to control the outbreak.

Per Country

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This is the same information presented as in the previous graphic, but with each country split into its own graph. This allows us to see the trajectory of effective R.

Most countries are decreasing, but we notice that Japan and Singapore are fluctuating, due to recent outbreaks.

Per Country (ribbons)

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This shows the uncertainty around the estimate of the effective R. We notice that as time goes on, there is less uncertainty around the estimate, so we can more confident in our estimate at these later times.

Australia

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Japan

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Cool!

South Korea

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China

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Cool!

Germany

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Spain

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France

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Italy

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Singapore

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United Kingdom

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USA

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Cool!

Explanation

The total number of incident cases arising at timestep \(t\), \(I_t\), is the sum of the numbers of incident local (\(I_{t}^{local}\)) and imported (\(I_{t}^{imported}\)) cases,

\[ I_t = I_t^{local} + I_t^{imported} \]

It is assumed that, if imported cases exist, they can be distinguished from local cases, for instance through epidemiological investigations, so that \(I_{t}^{local}\) and \(I_{t}^{imported}\) are observed at each timestep.

\[\Lambda_t(w_s) = \sum_{s=1}^t (I_{t-s}^{local} + I_{t-s}^{imported}) w_s = \sum_{s=1}^t I_{t-s} w_s \] \[ \mathbb E(I_t^{local} | I_0, I_1, \ldots, I_{t-1}, w_s, T_t) = R_t\Lambda_t (w_s)\]

NSW – locally-acquired & overseas-acquired cases treated separately
(cases under investigation excluded)
parametric serial interval distribution

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Commentary

NSW – locally-acquired & overseas-acquired cases treated separately
(cases under investigation excluded)
serial interval distribution estimated from data

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Commentary

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NSW – adjusting for potential under-ascertainment, locally-acquired & overseas-acquired cases treated separately, (cases under investigation excluded), parametric serial interval distribution

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In these plots, the counts of incident cases with presumed local sources of infection have been inflated by a factor of 10, and the counts of cases with presumed overseas sources of infection inflated by a factor of 1.5. This mimics ten-fold under-ascertainment of locally-transmitted cases, and 50% under-ascertainment of inbound cases.

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NSW – adjusting for potential under-ascertainment, locally-acquired & overseas-acquired cases treated separately, (cases under investigation excluded), serial interval distribution estimated from data

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In these plots, the counts of incident cases with presumed local sources of infection have been inflated by a factor of 10, and the counts of cases with presumed overseas sources of infection inflated by a factor of 1.5. This mimics ten-fold under-ascertainment of locally-transmitted cases, and 50% under-ascertainment of inbound cases.

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NSW – locally-acquired & overseas-acquired cases treated separately
(cases under investigation included)
parametric serial interval distribution

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Commentary

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NSW – locally-acquired & overseas-acquired cases treated separately
(cases under investigation included)
serial interval distribution estimated from data

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Commentary

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NSW – all cases treated as locally-acquired
parametric serial interval distribution

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From data commentary blah blah blah.

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NSW – all cases treated as locally-acquired
serial interval distribution estimated from data

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From data commentary blah blah blah.

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